According to Halacha, is shechita done by Jews with prosthetic arms kosher and valid? The reason I ask is that shechita has to be done by Jews: machine shechita is generally not valid. But in this case, the prosthetic arm is arguably an extension of the Jew and therefore is it valid or no?
Shulchan Aruch, Yoreh Deah 7.1 rules that if someone attaches a knife to a heavy wheel, gives the wheel a big spin (whether using their hand or foot to do so!), and then puts the animal's neck in its path, that's kosher shechitah as it's human-powered. Shulchan Aruch sounds like one is perfectly allowed to do so, in fact, if they know what they are doing. (Rabbi Ovadya Yosef mentions this as one possible source vis-a-vis machine matza. However Rabbi Ovadia cites sources that if a strong wind is also pushing the wheel, that would no longer be "human-powered.")
Thus if the prosthetic doesn't have a battery powering it, it's an easy "yes." If there's a battery powering it, we get into a more complex question of whether that's still considered "human powered" and/or the electronic limb is an extension of the person.
Shulchan Aruch continues that if a wheel is constantly being pushed by a river, that's not "human-powered" and would not be proper shechitah. However, if someone opened a dam which then immediately flowed to push the wheel, the wheel's first revolution is considered "human powered", but subsequent revolutions are not. We would not advise people to do shechitah with this first revolution, but after-the-fact, it is kosher shechita.
A strong case could thus be made that even with an electrically-boosted prosthetic, each time one's natural muscles (or nerves?) trigger, it would be considered "releasing the dammed-up" electrical current; if we were confident that the analogy is perfect (and I'm not), the apparent conclusion would be "we don't advise such slaughter, but it would be kosher after-the-fact." But that's going several steps out on a limb.